A train is moving along the tracks at a constant speed u . A girl on the train throws a ball of mass m straight ahead along the direction of motion of the train with speed v with respect to herself. T

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A train is moving along the tracks at a constant speed u . A girl on the train throws a ball of mass m straight ahead along the direction of motion of the train with speed v with respect to herself. Then

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Hint : w.r.t. the girl E k ​ = 2 1 ​ m v 2 ∴ W = Δ E k ​ = 1/2 mv 2 Work by the train = { 2 1 ​ ( v + u ) 2 − 2 1 ​ m u 2 } − 2 1 ​ m v 2 ​ = 2 1 ​ m ( v 2 + u 2 + 2 vu ) − 2 1 ​ m ( v 2 + u 2 ) = m vu ​ Gain in E k ​ = 2 1 ​ m ( v + u ) 2 − 2 1 ​ m u 2 = 2 1 ​ m v 2 + m vu measured from rail track

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